You also can buy an inexpensive "biscuit cutter" and "justify" it for this need, then you have one!! Dowels can be hard to line up, or you need a good dowel jig with inserts for various drill bit sizes which can be almost the same price
as a biscuit cutter
. Get some number 20 biscuits, or as large as you can fit...a biscuit cutter
will automatically line up the wood amazingly flush when you reassemble it...without any screws at all.
In my cabinet work I go through hundreds of biscuits and I find myself using biscuits in many weird applications (like yours) that I would not ordinarily do if I did not have one, but a biscuit cutter is a good investment..
Unless you want to go really nuts and get a tenoning jig...OK, back to reality,,biscuit cutter is fine.
As far as glue, normal yellow woodworkers glue marked "indoor or outdoor" should do fine. Joints made with biscuits and yellow wood glue will never break at the old joint, they always break tearing wood away from the joint on one side or the other. I say this after some mistakes
wishing I could break it at the old joint...never works..if I ever have to undo a mistake, I put it on the table saw and recut it.
Oh..a biscuit cutter will work even on a broken surface...the slot it cuts has a little of free play